how long will it take for 200000 $ to double @ 5% interest?

Answer 1

At Year 14, you'd have $415785.64. Of course, this presumes your interest isn't being taxed.

Answer 2

It is assumed that the interest would be applied annually and compounded annually. (If it is annual simple interest @5%, then obviously it would take 20 years to double the money.)
$1 @5% compounded annually would earn an interest of
$ 0.9799 (approx.) at the end of 14 years and $ 1.0789 (approx.) as interest after 15 years. Just multiply the capital invested by these figures to get the capital+interest amount that would be close to double the amount.